The US can't practically run out of cash as long as the world reserve currency is the USD. They can print money to pay their debts even to foreign countries. Of course that's a single use get-out-of-jail card. Because once they do that, the USD will cease to be the reserve currency.
Possibly at that point some "other" currency that is not controlled by any single government... perhaps something decentralized.
The question is what would be the alternative to the reserve currency US dollar for export-strong countries?
There is none. It would damage confidence massively, but in principle not much would change. There would be only two options as a reserve currency, that would be the Euro and the Yuan. But both have their weaknesses, and other currencies like the Yen or the Swiss Franc are too small to serve as a world reserve currency.